You win on the efficiency test too. with n = 100 we are roughly the same time, but as n gets large I get bogged down somewhere. I'm running a test with n = 1000000 on my dual proc, which has been hung for about five minutes now. But based on the out put I've already seen for smaller n's, I suspect that you will slaughter me time wise.

I don't understand why yours is faster because you use two for loops and I use a while loop the second time, dropping the overhead of making the temp array that foreach generates. Now I'm curious about the efficiencies of the two looping mechanisms...

I suspect that it isn't my looping structure, but that
I'm stepping across the primes low to high and you're
going high to low. My code tests division by '2' first,
so the inner loop only runs once half of the time. Thus
only runs twice a third of the time, 4 times a fifth of
the time, etc.

since you test the large numbers first, you have to make more
tests to throw out a potential prime.

Although what I propose may not be the "classic" sieve algorithm, in truth you only need to test up to the primes which are less than the square root of the target number. In other words, you need not divide by any primes greater than 4 when testing 16. Based on the associative property of multiplication, if you can show that no numbers <= sqrt(n) evenly divide n, then you have also shown that there are no numbers => sqrt(n) which evenly divide n.
While this may add a few chars to your code, it reduces the compute time enormously when you get to large n's.

Update: Actually, it doesn't look like ANY of us are implenting the true Sieve algorithm. The algorithm can be found here: http://www.math.utah.edu/~alfeld/Eratosthenes.html. It does in fact use the sqrt(n) modification, but doesn't do divide-testing ... instead it does "weeding out" of multiples. Same result, different technique.

When putting a smiley right before a closing parenthesis, do you:

Use two parentheses: (Like this: :) )
Use one parenthesis: (Like this: :)
Reverse direction of the smiley: (Like this: (: )
Use angle/square brackets instead of parentheses
Use C-style commenting to set the smiley off from the closing parenthesis
Make the smiley a dunce: (:>
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